I have a Kerv payment ring and it works in exactly the same way with NFC readers. If the door lock could read your old ring, it will be able to read the payement ring with no issues.
I was enjoying unlocking my phone with my payment ring until Google disabled the feature in Oreo, boo.
No surprise it doesn't work with Apple. They would want to sell you an iRing at three times the price, then claim that it's new groundbreaking technology invented by them, like, err, contactless charging...